Jackie Kennedy in the Early Sixties: Making of an American Icon

It was in those brief, heady years or perhaps it was really just one year, during the campaign and election of 1960—when John F. Kennedy and his young, beautiful wife were fast becoming national and then international celebrities that the legend of Jackie was born.

Looking back now, even in the light of all we know about her fraught, strained, "storybook" marriage to an obsessively philandering husband, there does seem to be something special about Jackie Kennedy. Maybe it's just that the camera loved her. Maybe she was so intriguing to so many people simply because, set beside the other prominent women in Washington, DC, in the early 1960s, she was young (barely in her 30s), chic and, with her Irish and French ancestry, indefinably and refreshingly "exotic."

But whatever the reasons behind her appeal, and however concrete or ineffable they might be, the fact remains that for millions of women around the globe, across generations, the woman in the White House in the Oleg Cassini outfits (made expressly for her), throwing formal dinner parties for artists, writers, scientists and diplomats, traveling the world, was the face not only of a new era but of an utterly new type of American woman. She was, somehow, at once warm and elegant, youthful and sophisticated, fun-loving and serious—and on top of it all, self-deprecatingly funny.

"The one thing I do not want to be called is 'first lady,'" she once said. "It sounds like a saddle horse."

Her husband, for his part, not only took his wife's enormous popularity in stride, but humbly acknowledged that, at times, he necessarily played second fiddle. After Jackie (who spoke fluent French) enjoyed a rapturous reception during a May 1961 trip to Paris, John Kennedy famously joked at a dinner: "I do not think it altogether inappropriate to introduce myself—I am the man who accompanied Jacqueline Kennedy to Paris, and I have enjoyed it."

Here, LIFE.com offers a selection of pictures—none of which ran in LIFE magazine— from that time in her life when she was first known to a rapt world, simply, as Jackie.

Jacqueline Kennedy Onassis died of complications from cancer in 1994. She was just 64 years old. "My mother died surrounded by her friends and her family and her books, and the people and the things that she loved," her son, John Jr., said. "She did it in her own way, and on her own terms, and we all feel lucky for that."